In this specification we are concerned with axial flux permanent magnet machines. Broadly speaking these have disc- or ring-shaped rotor and stator structures arranged about an axis. Typically the stator comprises a set of coils each parallel to the axis and the rotor bears a set of permanent magnets and is mounted on a bearing so that it can rotate about the axis driven by fields from the stator coils. FIG. 1a shows the general configuration of an axial flux machine with a pair of rotors R1, R2 to either side of a stator S—although a simple structure could omit one of the rotors. As can be seen there is an air gap G between a rotor and a stator and in an axial flux machine the direction of flux through the air gap is substantially axial.
There are various configurations of axial flux permanent magnet machine depending upon the arrangement of north and south poles on the rotors. FIG. 1b illustrates the basic configurations of a Torus NS machine, a Torus NN machine (which has a thicker yoke because the NN pole arrangement requires flux to flow through the thickness of the yoke), and a YASA (Yokeless and Segmented Armature) topology. The illustration of the YASA topology shows cross-sections through two coils, the cross-hatched area showing the windings around each coil. As can be appreciated, dispensing with the stator yoke provides a substantial saving in weight and iron losses, but one drawback is loss of a route for heat to escape from stator coils. Thus preferably coolant for the machine is circulated through the stator housing.
We have previously described, in WO2012/022974, a clamshell type stator housing. Advantageously shoes of the stator bars on which the stator coils are wound are overmoulded into the radial wall of the housing. Thus the housing provides both structural strength and a coolant chamber.
Referring first to FIGS. 1c, 2 and 3, which are taken from our PCT application WO2012/022974, FIG. 1c shows a schematic illustration of a yokeless and segmented armature machine 10. The machine 10 comprises a stator 12 and two rotors 14a,b. The stator 12 is a collection of separate stator bars 16 spaced circumferentially about a rotation axis 20 of the rotors 14a,b. Each bar 16 has its own axis (not shown) which is preferably, but not essentially, disposed parallel to the rotation axis 20. Each end of each stator bar is provided with a shoe 18a,b which serves a physical purpose of confining a coil stack 22, which stack 22 is preferably of square/rectangular section insulated wire so that a high fill factor can be achieved. The coils 22 are connected to an electrical circuit (not shown) that, in the case of a motor, energizes the coils so that the poles of the resultant magnetic fields generated by the current flowing in the coils is opposite in adjacent stator coils 22. In the alternative arrangements non-YASA topologies of FIG. 1b the stator coils are wound around one or more stator teeth whereas in the YASA topology of FIG. 1c they are wound around respective stator bars.
The two rotors 14a,b carry permanent magnets 24a, b that face one another with the stators coil 22 between (when the stator bars are inclined—not as shown—the magnets are likewise). Two air gaps 26a,b are disposed between respective shoe and magnet pairs 18a/24a, 18b/24b. 
In a motor the coils 22 are energized so that their polarity alternates serving to cause coils at different times to align with different magnet pairs, resulting in torque being applied between the rotor and the stator. The rotors 14a,b are generally connected together (for example by a shaft, not shown) and rotate together about the axis 20 relative to the stator 12. The magnetic circuit 30 is provided by two adjacent stator bars 16 and two magnet pairs 24a,b and a back iron 32a,b for each rotor links the flux between the back of each magnet 24a,b facing away from the respective coils 22. The stator coils 16 are enclosed within a housing that extends through the air gap 26a, b and which defines a chamber supplied with a cooling medium.
Turning to FIG. 3, a stator 12a is shown in which the stator coils are located between plastics material clam shells 42a, b. These clamshells have external cylindrical walls 44, internal cylindrical walls 46, and annular radially disposed walls 48. In the prior art example of FIG. 3 the radial walls 48 include internal pockets 50 to receive the shoes 18a,b of the stator bars 16 and serve to locate the stator coil assemblies 16, 22, 18a,b when the two clam shell housings 42a, b of the stator 12a are assembled together. The stator housing 42a, b defines spaces 52 internally of the coils 22 and externally at 54 around the outside of the coils 22 and there are spaces 56 between the coils defining a cooling chamber within the housing through which coolant is pumped.
In a typical machine an even number of coils (divisible by 3 for a 3 phase machine) and an even number of magnets is spaced around the axis of rotation 20. In addition there are different numbers of coils and magnets, so that the coils do not all come into registration with the corresponding magnet pair at the same time and at the same rotational position of the rotor with respect to the stator. This serves to reduce cogging torque and benefits continuous torque creation. However further improvements in cogging reduction are desirable. In addition similar considerations to those which affect cogging also affect the shape of the back emf of a motor and it is generally desirable to make the back emf as sinusoidal as practicable, thus reducing the total harmonic distortion of the machine. General background prior art can be found in US2011/309706.